Question

The ratio of the areas of two triangles is equal to the square of the ratio of their corresponding sides. Then these triangles will be:

• A. Equilateral
• B. Scalene
• C. Similar
• D. Isosceles

Hint:

For similar triangles, the ratio of their areas is the square of the ratio of their corresponding sides.

Answer 1

The Correct Option is C

Step 1: Understanding the relationship between the areas and sides of similar triangles.
For two triangles, if the ratio of their areas is equal to the square of the ratio of their corresponding sides, then the triangles must be similar. This is a property of similar triangles where the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Step 2: Apply the property.
If the ratio of areas \( \frac{A_1}{A_2} \) is given by \( \left(\frac{s_1}{s_2}\right)^2 \), where \( s_1 \) and \( s_2 \) are the corresponding sides of the triangles, then the two triangles must be similar. This is based on the principle that similar triangles have proportional sides and their areas are related by the square of the ratio of corresponding sides.
Step 3: Conclusion.
Therefore, the two triangles are similar.